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Chapter 15: Q3MP (page 776)

There are 3 red and 2 white balls in one box and 4 red and 5 white in the second box. You select a box at random and from it pick a ball at random. If the ball is red, what is the probability that it came from the second box?

Short Answer

Expert verified

The Probability is found to be p(S/R)=2047and it can be shown with the picture given below.

Step by step solution

01

Given Information. 

It has been given that there are 3 red and 2 white balls in one box and 4 red and 5 white in the second box.

02

 Step 2: Definition of Probability.

Probability means the chances of any event to occur is called it probability.

03

Find the probability.

Find the Probability of the red ball.

p(R)=p1R+p2R=0.5×35+0.5×49=4790n

If the ball is red the probability that it comes from the second box is derived below.

p(S/R)=p(SR)p(R)=0.5×4947/90=2047

04

Draw the diagram to show the situation. 

The situation is shown below.

The Probability is shown below.

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Most popular questions from this chapter

(a) Find the probability that in two tosses of a coin, one is heads and one tails. That in six tosses of a die, all six of the faces show up. That in12tosses of a12 -sided die, all12 faces show up. That in n tosses of an n-sided die, all n faces show up.

(b) The last problem in part (a) is equivalent to finding the probability that, when n balls are distributed at random into n boxes, each box contains exactly one ball. Show that for large n, this is approximatelye−n2πn.

(a) Find the probability density function f(x)for the position x of a particle which is executing simple harmonic motion on (−a,a)along the x axis. (See Chapter 7 , Section 2 , for a discussion of simple harmonic motion.) Hint: The value of x at time t is x=acosωt. Find the velocity dxdt ; then the probability of finding the particle in a given dx is proportional to the time it spends there which is inversely proportional to its speed there. Don’t forget that the total probability of finding the particle somewhere must be 1.

(b) Sketch the probability density function f(x)found in part (a) and also the cumulative distribution function f(x) [see equation (6.4)].

(c) Find the average and the standard deviation of x in part (a).

A basketball player succeeds in making a basket 3 tries out of 4. How many tries arenecessary in order to have probability >0.99of at least one basket?

A letter is selected at random from the alphabet. What is the probability that it is one of the letters in the word “probability?” What is the probability that it occurs in the first half of the alphabet? What is the probability that it is a letter after x?

Computer plot on the same axes the normal density functions with μ=0σ=1and, 2, and 5. Label each curve with itsσ.
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